Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_219a5692ece616b4a88502d80a85b644180cde982b21251f92a23d11d1a5d022 with
setminus (binintersect x0 x1) x2,
binintersect x0 (setminus x1 x2) leaving 2 subgoals.
Let x3 of type ι be given.
Apply unknownprop_e02b92c94ff70655b8eb0623a7ec106c0c0c9c65ac0f52f9689f2e6c9f563b5d with
binintersect x0 x1,
x2,
x3,
In x3 (binintersect x0 (setminus x1 x2)) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_9f9c1680d203bdbb862d1bf6c2b8504d7e3a6fca72f77bd8968e86ad6ad69346 with
x0,
x1,
x3,
In x3 (binintersect x0 (setminus x1 x2)) leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_7e73699eda4c2a35af8db1aea1ddace7d2346405cd3944ace259823e1ec33cf3 with
x0,
setminus x1 x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply unknownprop_3fe7f97dcb00bcf31cf989081bd8403f8f0647acc7dd719f8a7da64cd4837dac with
x1,
x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H2.
Let x3 of type ι be given.
Apply unknownprop_9f9c1680d203bdbb862d1bf6c2b8504d7e3a6fca72f77bd8968e86ad6ad69346 with
x0,
setminus x1 x2,
x3,
In x3 (setminus (binintersect x0 x1) x2) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_e02b92c94ff70655b8eb0623a7ec106c0c0c9c65ac0f52f9689f2e6c9f563b5d with
x1,
x2,
x3,
In x3 (setminus (binintersect x0 x1) x2) leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_3fe7f97dcb00bcf31cf989081bd8403f8f0647acc7dd719f8a7da64cd4837dac with
binintersect x0 x1,
x2,
x3 leaving 2 subgoals.
Apply unknownprop_7e73699eda4c2a35af8db1aea1ddace7d2346405cd3944ace259823e1ec33cf3 with
x0,
x1,
x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H4.